EA-10/16 - National Physical Laboratory

EA-10/16 • EA Guidelines on the Estimation of Uncertainty in Hardness Measurements
c
i
∆H
≈
∆x
i
X 1 = x1 ,..., X n = x n
(2)
The experimental evaluation of the sensitivity coefficients is usually
time consuming, therefore usually it is advantageous to use the
experimental results given in literature [4, 5] and adopted for the
examples attached, but one shall be careful when the relevant
factors depend on the characteristics of the material tested (dwell
time and indentation velocity). In this case some experiments with
the specific material are necessary.
u i (H) is the contribution to the standard uncertainty associated with the
hardness H resulting from the standard uncertainty u(x i ) associated
with the input estimate x i :
u
u i (H) = c i u(x i ) (3)
d) For uncorrelated input quantities the square of the standard
uncertainty u(H) associated with the measured hardness H is given
by:
2
n
∑
2
( H ) = u i
( H )
(4)
i=
1
e) Calculate for each input quantity X i the contribution u i (H) to the
uncertainty associated with the hardness H resulting from the input
estimate x i according to Eqs. (2) and (3) and sum their squares as
described in Eq. (4) to obtain the square of the standard uncertainty
u(H) of the hardness H.
f) Calculate the expanded uncertainty U by multiplying the standard
uncertainty u(H) associated with the hardness H by a coverage
factor k=2:
U = ku(H) (5)
Should the effective degrees of freedom ν eff in exceptional cases be
less than 15, then calculate the coverage factor k according to
EA/4-02, Annex E [1].
g) Report the result of the measurement as follows: in calibration
certificates, the complete result of the measurement comprising the
estimate H of the measurand and the associated expanded
uncertainty U shall be given in the form (H±U). To this an
explanatory note must be added which in the general case should
have the following content:
The reported expanded uncertainty of measurement has been
obtained by multiplying the combined standard uncertainty by the
coverage factor k=2 that, for a normal distribution, corresponds to a
confidence level p of approximately 95%. The combined standard
uncertainty of measurement has been determined in accordance
with EA/4-02 [1].
July 05 rev.00 Page 12 of 24